Question: Solve for $x$ and $y$ using elimination. $\begin{align*}-8x+5y &= 5 \\ 7x-5y &= -1\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-x = 4$ Divide both sides by $-1$ and reduce as necessary. $x = -4$ Substitute $-4$ for $x$ in the top equation. $-8( -4)+5y = 5$ $32+5y = 5$ $5y = -27$ $y = -\dfrac{27}{5}$ The solution is $\enspace x = -4, \enspace y = -\dfrac{27}{5}$.